Original synthetic study
The productivity gain from doubling permeability in a synthetic case
Doubling permeability doubles steady radial rate in this controlled case. That proportional gain follows from the equation when pressure boundaries, fluid properties, geometry and skin are unchanged.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Make the counterfactual explicit
This study keeps 500 psi drawdown, 50 ft pay, 2 cP viscosity, Bo = 1.2, fixed radii and skin = 2. Permeability is the only varying input.
Each rate is calculated by the site's published steady radial relationship. The experiment is synthetic; it is not a stimulation result or a matched field-well comparison.
Use the ratio as an independent check
Because k appears linearly in the numerator, q2/q1 must equal k2/k1. The common denominator cancels. A failure of this ratio check would indicate inconsistent controls or arithmetic.
Productivity index q/Δp also doubles on the same conditions. It remains a model inflow coefficient rather than a prediction of the installed system's operating point.
Explain the limits of the result
A real permeability change can accompany skin changes, multiphase effects or pressure-dependent rock behavior. The controlled study does not include those mechanisms.
Use the downloaded values to test proportionality, then change one additional assumption in the calculator to see why unmatched scenarios no longer support a permeability-only attribution.
Explore the example
Replayed with the same equation record and calculation engine as /calculators/steady-state-radial-liquid-flow-rate. Original synthetic inputs; engine outputs are saved in the downloadable record.
Select one of 5 recorded scenarios. Intermediate states are not interpolated.
Permeability (mD) = 100. q_o (STB/day): 735.844574.
- q_o (STB/day)
Worked example
Steady-State Radial Liquid Flow Rate
Fixed controls: h = 50 ft; p_e = 3000 psi; p_wf = 2500 psi; mu_o = 2 cP; B_o = 1.2 bbl/STB; r_e = 1000 ft; r_w = 0.328 ft; s = 2 dimensionless. k is varied as shown.
Relation and unit basis
q_o = 0.00708 k h (p_e - p_wf) / (mu_o B_o (ln(r_e / r_w) + s))
k: Permeability (mD). h: Net Pay Thickness (ft). p_e: External Boundary Pressure (psi). p_wf: Flowing Bottom-Hole Pressure (psi). mu_o: Oil Viscosity (cP). B_o: Oil Formation Volume Factor (bbl/STB). r_e: Drainage Radius (ft). r_w: Wellbore Radius (ft). s: Skin Factor (dimensionless).
1. Define the baseline
Permeability (mD) = 100
Fixed controls: h = 50 ft; p_e = 3000 psi; p_wf = 2500 psi; mu_o = 2 cP; B_o = 1.2 bbl/STB; r_e = 1000 ft; r_w = 0.328 ft; s = 2 dimensionless. k is varied as shown.
2. Select the relation
q_o = 0.00708 k h (p_e - p_wf) / (mu_o B_o (ln(r_e / r_w) + s))
k: Permeability (mD). h: Net Pay Thickness (ft). p_e: External Boundary Pressure (psi). p_wf: Flowing Bottom-Hole Pressure (psi). mu_o: Oil Viscosity (cP). B_o: Oil Formation Volume Factor (bbl/STB). r_e: Drainage Radius (ft). r_w: Wellbore Radius (ft). s: Skin Factor (dimensionless).
3. Substitute the values
k = 100; h = 50; p_e = 3000; p_wf = 2500; mu_o = 2; B_o = 1.2; r_e = 1000; r_w = 0.328; s = 2 → q_o = 735.844574 STB/day
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
q_o (STB/day) = 735.844574
Stock-tank liquid rate changes linearly with k on the stated steady boundary and Bo basis.
Result and interpretation
q_o (STB/day) = 735.844574
Stock-tank liquid rate changes linearly with k on the stated steady boundary and Bo basis.
Read this as a one-variable experiment. The linked calculator accepts broader scenarios, which need their own interpretation.
Study data and reproduction
Replayed with the same equation record and calculation engine as /calculators/steady-state-radial-liquid-flow-rate. Original synthetic inputs; engine outputs are saved in the downloadable record.
| Permeability (mD) | q_o (STB/day) |
|---|---|
| 25 | 183.9611 |
| 50 | 367.9223 |
| 100 | 735.8446 |
| 200 | 1,471.689 |
| 400 | 2,943.378 |
Scroll the table to see all columns. The highlighted row is the worked baseline. Downloads retain full numerical precision.
Test your understanding
Work through the question before revealing its answer. Use the stated assumptions and include units in every numerical step.
1. If rate does not double after k doubles in a comparison, what should be checked first?
Show the worked answer
Check whether drawdown, skin, viscosity, Bo, thickness or geometry also changed before attributing the difference to nonlinearity.
2. Reproduce the baseline q_o (STB/day) without rounding intermediate values.
Show the worked answer
k = 100; h = 50; p_e = 3000; p_wf = 2500; mu_o = 2; B_o = 1.2; r_e = 1000; r_w = 0.328; s = 2 → q_o = 735.844574 STB/day. q_o (STB/day) = 735.844574. Stock-tank liquid rate changes linearly with k on the stated steady boundary and Bo basis.
3. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
Permeability (mD) changes from 25 to 400. Other controls remain as stated in the premise. q_o (STB/day) changes from 183.961144 to 2943.3783.
4. What would be needed to apply this example to a different physical system?
Show the worked answer
Replace the synthetic controls with compatible documented inputs and check the relation's assumptions. k: Permeability (mD). h: Net Pay Thickness (ft). p_e: External Boundary Pressure (psi). p_wf: Flowing Bottom-Hole Pressure (psi). mu_o: Oil Viscosity (cP). B_o: Oil Formation Volume Factor (bbl/STB). r_e: Drainage Radius (ft). r_w: Wellbore Radius (ft). s: Skin Factor (dimensionless). Stock-tank liquid rate changes linearly with k on the stated steady boundary and Bo basis.
Before using the result
- Retain all stated controls.
- Check q ratios against k ratios.
- Do not treat synthetic gain as field validation.
Stock-tank liquid rate changes linearly with k on the stated steady boundary and Bo basis.
Continue learning
Start with the broader workflow guide · Related method guide
Sources and method
The explanation and synthetic examples are original PetroCalcHub teaching material. The references below support the definitions and model context. They do not supply field validation for the synthetic scenarios.